Grad-Shafranov Reconstruction Research Articles

A Closer Look at Small-scale Magnetic Flux Ropes in the Solar Wind at 1 au: Results from Improved Automated Detection

Small-scale interplanetary magnetic flux ropes (SMFRs) are similar to ICMEs in magnetic structure, but are smaller and do not exhibit coronal mass ejection plasma signatures. We present a computationally efficient and GPU-powered version of the single-spacecraft automated SMFR detection algorithm based on the Grad–Shafranov (GS) technique. Our algorithm can process higher resolution data, eliminates selection bias caused by a fixed 〈B〉 threshold, has improved detection criteria demonstrated to have better results on an MHD simulation, and recovers full 2.5D cross sections using GS reconstruction. We used it to detect 512,152 SMFRs from 27 yr (1996–2022) of 3 s cadence Wind measurements. Our novel findings are the following: (1) the SMFR filling factor (∼ 35%) is independent of solar activity, distance to the heliospheric current sheet, and solar wind plasma type, although the minority of SMFRs with diameters greater than ∼0.01 au have a strong solar activity dependence; (2) SMFR diameters follow a log-normal distribution that peaks below the resolved range (≳104 km), although the filling factor is dominated by SMFRs between 105 and 106 km; (3) most SMFRs at 1 au have strong field-aligned flows like those from Parker Solar Probe measurements; (4) the radial density (generally ∼1 detected per 106 km) and axial magnetic flux density of SMFRs are higher in faster solar wind types, suggesting that they are more compressed. Implications for the origin of SMFRs and switchbacks are briefly discussed. The new algorithm and SMFR dataset are made freely available.

Characterization of Magnetic Flux Contents for Two Flux Transfer Events From Both In Situ and Ionospheric Observations

AbstractFlux transfer events (FTEs) are a type of magnetospheric phenomena that exhibit distinctive observational signatures from the in situ spacecraft measurements. They are generally believed to possess a magnetic field configuration of a magnetic flux rope and formed through magnetic reconnection at the dayside magnetopause, sometimes accompanied with enhanced plasma convection in the ionosphere. We examine two FTE intervals under the condition of southward interplanetary magnetic field (IMF) with a dawn‐dusk component. We apply the Grad‐Shafranov (GS) reconstruction method to the in situ measurements by the Magnetospheric Multiscale (MMS) spacecraft to derive the magnetic flux contents associated with the FTE flux ropes. In particular, given a cylindrical magnetic flux rope configuration derived from the GS reconstruction, the magnetic flux content can be characterized by both the toroidal (axial) and poloidal fluxes. We then estimate the amount of magnetic flux (i.e., the reconnection flux) encompassed by the area “opened” in the ionosphere, based on the ground‐based Super Dual Auroral Radar Network (SuperDARN) observations. We find that for event 1, the FTE flux rope is oriented in the approximate dawn‐dusk direction, and the amount of its total poloidal magnetic flux falls within the range of the corresponding reconnection flux. For event 2, the FTE flux rope is oriented in the north‐south direction. Both the FTE flux and the reconnection flux have greater uncertainty. We provide a detailed description about a formation scenario of sequential magnetic reconnection between adjacent field lines based on the FTE flux rope configurations from our results.

Electron magnetohydrodynamics Grad–Shafranov reconstruction of the magnetic reconnection electron diffusion region

We present a study of the electron magnetohydrodynamics Grad–Shafranov (GS) reconstruction of the electron diffusion region (EDR) of magnetic reconnection. Two-dimensionality of the magnetoplasma configuration and steady state are the two basic assumptions of the GS reconstruction technique, which represent the method’s fundamental limitations. The present study demonstrates that the GS reconstruction can provide physically meaningful results even when these two assumptions, which are hardly fulfilled in spacecraft observations, are violated. This conclusion is supported by the reconstruction of magnetic configurations of two EDRs, encountered by the Magnetospheric Multiscale (MMS) Mission on July 11, 2017 and September 8, 2018. Here, the former event exhibited a violation of two-dimensionality, and the latter event exhibited a violation of steady state. In both cases, despite the deviations from the ideal model configuration, reasonable reconstruction results are obtained by implementing the herein introduced compressible GS reconstruction model. In addition to the discussed fundamental limitations, all existing versions of the GS reconstruction technique rely on a number of minor simplifying assumptions, which restrict the model scope and efficiency. We study the prospects for further model improvement and generalization analytically. Our analysis reveals that nearly all these minor limitations can be overcome by using a polynomial MMS-tailored reconstruction technique in the space of rotationally invariant variables instead of Cartesian coordinates.

Ion-Scale Magnetic Flux Rope Generated From Electron-Scale Magnetopause Current Sheet: Magnetospheric Multiscale Observations.

We present in-depth analysis of three southward-moving meso-scale (ion-to magnetohydrodynamic-scale) flux transfer events (FTEs) and subsequent crossing of a reconnecting magnetopause current sheet (MPCS), which were observed on 8 December 2015 by the Magnetospheric Multiscale spacecraft in the subsolar region under southward and duskward magnetosheath magnetic field conditions. We aim to understand the generation mechanism of ion-scale magnetic flux ropes (ISFRs) and to reveal causal relationship among magnetic field structures, electromagnetic energy conversion, and kinetic processes in magnetic reconnection layers. Results from magnetic field reconstruction methods are consistent with a flux rope with a length of about one ion inertial length growing from an electron-scale current sheet (ECS) in the MPCS, supporting the idea that ISFRs can be generated through secondary reconnection in an ECS. Grad-Shafranov reconstruction applied to the three FTEs shows that the FTEs had axial orientations similar to that of the ISFR. This suggests that these FTEs also formed through the same secondary reconnection process, rather than multiple X-line reconnection at spatially separated locations. Four-spacecraft observations of electron pitch-angle distributions and energy conversion rate suggest that the ISFR had three-dimensional magnetic topology and secondary reconnection was patchy or bursty. Previously reported positive and negative values of , with magnitudes much larger than expected for typical MP reconnection, were seen in both magnetosheath and magnetospheric separatrix regions of the ISFR. Many of them coexisted with bi-directional electron beams and intense electric field fluctuations around the electron gyrofrequency, consistent with their origin in separatrix activities.

Small-scale Magnetic Flux Ropes in Stream Interaction Regions from Parker Solar Probe and Wind Spacecraft Observations

Using in situ measurements from the Parker Solar Probe and Wind spacecraft, we investigate the small-scale magnetic flux ropes (SFRs) and their properties inside stream interaction regions (SIRs). Within SIRs from ∼0.15 to 1 au, SFRs are found to exist in a wide range of solar wind speeds with more frequent occurrences after the stream interface, and the Alfvénicity of these structures decreases significantly with increasing heliocentric distances. Furthermore, we examine the variation of five corresponding SIRs from the same solar sources. The enhancements of suprathermal electrons within these SIRs persist at 1 au and are observed multiple times. An SFR appears to occur repeatedly with the recurring SIRs and is traversed by the Wind spacecraft at least twice. This set of SFRs has similarities in variations of the magnetic field components, plasma bulk properties, density ratio of solar wind alpha and proton particles, and unidirectional suprathermal electrons. We also show, through the detailed time-series plots and Grad–Shafranov reconstruction results, that they possess the same chirality and carry comparable amounts of magnetic flux. Lastly, we discuss the possibility for these recurring SFRs to be formed via interchange reconnection, maintain the connection with the Sun, and survive up to 1 au.

Reconnection Outflow Reversal Associated with Ion-scale Magnetic Flux Ropes in the Earth's Midtail: ARTEMIS Observations and Reconstruction Results

A rare reconnection outflow reversal in the Earth's midtail observed by the two Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) probes, is presented. During the event, two ion-scale magnetic flux ropes were separately observed by THC in the earthward and tailward reconnection outflows that were adjacent and accompanied, respectively, by the positive and negative normal magnetic field components to the current sheet. The two flux ropes were separated by ∼2.75 minutes and at the center of the flux ropes, the magnetic field strength was enhanced with a large core field. Comparison results of the convection and measured electric fields reveal that the ions and the magnetic fields were decoupled in the regions surrounding the two flux ropes. The two-dimensional magnetic field maps from the Grad–Shafranov reconstruction show that the diameters of the two flux ropes were similar, being ∼7.1 and ∼7.9 ion inertial lengths, but the aspect ratios of the width to the length were different, being ∼0.35 and ∼0.47. Moreover, one of the reconstructed field maps suggests that multiple x-lines may exist in the midtail reconnection and that the traveling compression region of the flux rope was seen at THB. The angle between the axial orientations of the two flux ropes was large, being ∼55°, and their axes were tilted away from the direction of the reconnection guide field, in agreement with the earlier studies of the magnetotail flux ropes.

Investigating Particle Acceleration by Dynamic Small-scale Flux Ropes behind Interplanetary Shocks in the Inner Heliosphere

We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find that second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.

Effects of Pressure Anisotropy on the Geometry of Magnetic Flux Rope

This paper aims to examine the effects of pressure anisotropy on the geometry of magnetic flux rope using the newly developed two-dimensional magnetohydrostatic reconstruction associated with pressure anisotropy. A small-scale magnetic flux rope observed by the Magnetospheric Multiscale mission, in the magnetosheath reconnection outflow during an outbound magnetopause crossing, is demonstrated. At the center of the flux rope, the magnetic field strength was enhanced with decreasing plasma pressure. The entire flux rope was mostly occupied by the pressure anisotropy of p ⊥ > p ∥, where the subscripts ∥ and ⊥ denote the components parallel and perpendicular to the local magnetic field, respectively. The estimated aspect ratio of the width to the length of the flux rope from reconstruction was ∼0.326 for p ⊥ > p ∥ and ∼0.389 for isotropic pressure. By comparing the magnetic field map from the isotropic Grad–Shafranov reconstruction, the results show for p ⊥ > p ∥ that (1) the width of the flux rope is reduced, leading to a small aspect ratio of the flux rope, and (2) the circular field line of the flux rope is contracted. Moreover, an experiment is conducted for p ∥ > p ⊥ by exchanging p ⊥ and p ∥ of the flux rope, for which the isotropic pressure is less affected. The experimental results indicate that the effects of p ∥ > p ⊥ on the geometry of the flux rope are opposite to that of p ⊥ > p ∥. The overall finding may provide new insight into charged particle acceleration within magnetic flux ropes/islands in anisotropic plasmas.

Evidence of Magnetic Reconnection with Multiple X Lines and Flux Ropes in Thin Magnetotail Currents Observed by the MMS Spacecraft: Results of Grad–Shafranov Reconstruction

Abstract There is some observational evidence for the existence of multiple X line magnetic reconnection (MR) in various planetary magnetotails but the overall observationally based MR topology in two or three dimensions is still not available. This study reports the first 2D structures of MR with multiple X lines and magnetic islands observed by the Magnetospheric Multiscale (MMS) spacecraft in the Earth’s magnetotail based on the Grad–Shafranov (GS) reconstruction model with temperature anisotropy. The tearing mode geometry is revealed within the spatial domain of 3800 km × 800 km with multiple X lines and magnetic islands on the spatial scale of the sub-ion inertial length or a few times the electron gyroradius. The MR event is seen by all four MMS spacecraft but the magnetic islands are caught only by the MMS3 spacecraft, and exhibit large firehose-type temperature anisotropy. The GS reconstructed maps based on the MMS1, 2, and 4 show a single X line and partial ion-scale magnetic islands with a smaller degree of temperature anisotropy. The reconstruction results remain the same for various energy closures, and the firehose-type anisotropy is found to yield smaller magnetic islands than the isotropic cases, which is opposite to the previous findings for MR events with mirror-type temperature anisotropy.

Mirror Mode Waves Immersed in Magnetic Reconnection

Abstract Mirror mode waves with anticorrelated density and magnetic field are widely observed in the heliosphere. This paper presents the first evidence of mirror mode waves occurring in the vicinity of a magnetic reconnection site (X-line) at the interface between the solar wind and Earth’s magnetosphere based on the analyses of two Magnetospheric Multiscale (MMS) crossing events along with the Grad–Shafranov (GS) reconstruction model with temperature anisotropy. The GS scheme solves the steady two-dimensional MHD equations in the frame of references moving with the plasma by using the spacecraft measurements. Both events have mirror type of pressure anisotropy and correspond, respectively, to the symmetric and asymmetric Harris type current sheets with the total thermal and magnetic field pressures being approximately constant. The GS reconstruction results show the magnetic reconnection with X line geometry associated with the mirror mode structures on the spatial lengths of 170 ∼ 370 km or 1.3 ∼ 3 ion gyroradius. The coexistence of mirror waves and magnetic reconnection provides the first observational evidence for the prior theoretical prediction of mixed tearing and mirror instabilities in plasma current sheets with temperature anisotropy.

Mirror-wave Structures in the Solar Wind: Grad–Shafranov Reconstruction, MHD, and Hall MHD Simulations with Double-polytropic Energy Closures

Abstract Mirror-mode waves with anticorrelated density and magnetic field are widely observed in the solar wind and planetary magnetospheres. In this study we analyze the characteristics of three mirror-wave events observed by the Magnetospheric Multiscale Mission in the Earth’s magnetosheath based on the Grad–Shafranov (GS) reconstruction model with temperature anisotropy. The GS scheme solves steady, two-dimensional MHD equations with field-aligned flow from the plasma and magnetic field measurements taken by a single spacecraft traversing across a coherent field structure. The reconstructed 2D plasma and field maps are obtained in the de Hoffmann–Teller frame and on the plane perpendicular to the invariant axis. The energy closures are a set of empirical energy laws with two polytropic exponents inferred from the observed mirror events which are in the ranges of and . It is shown that the mirror waves are nonpropagating with linear magnetic field polarization and possess anticorrelated density, temperatures, and magnetic field with the widths of 10–40 ion inertial lengths. The double-polytropic MHD and Hall MHD simulations of mirror instability show consistent results with the GS reconstructions in terms of field-line geometry, phase relations and the sizes of mirror waves, etc.

A New Method to Model Magnetic Cloud-driven Forbush Decreases: The 2016 August 2 Event

Abstract Interplanetary coronal mass ejections (ICMEs), generally containing magnetic clouds (MCs), are associated with galactic-cosmic ray (GCR) intensity depressions known as Forbush decreases (FDs). An ICME was observed at L1 between 2016 August 2 at 14:00 UT and August 3 at 03:00 UT. The MC region was identified and its magnetic configuration was retrieved by using the Grad–Shafranov (GS) reconstruction. A weak FD in the GCR count-rate was observed on 2016 August 2 by a particle detector on board the European Space Agency LISA Pathfinder mission. The spacecraft orbited around L1 and the particle detector allowed us to monitor the GCR intensity at energies above 70 MeV n −1. A 9% decrease in the cosmic-ray intensity was observed during the ICME passage. The first structure of the ICME caused a 6.4% sharp decrease, while the MC produced a 2.6% decrease. A suited full-orbit test-particle simulation was performed on the MC configuration obtained through the GS reconstruction. The FD amplitude and time profile obtained through the simulation show an excellent agreement with observations. The test-particle simulation allows us to derive the energy dependence of the MC-driven FD providing an estimate of the amplitude at different rigidities, here compared with several neutron monitor observations. This work points out the importance of the large-scale MC configuration in the interaction between GCRs and ICMEs and suggests that particle drifts have a primary role in modulating the GCR intensity within the MC under study and possibly in at least all slowly expanding ICMEs lacking a shock/sheath region.

Grad–Shafranov reconstruction of the magnetic configuration in the reconnection X-point vicinity in compressible plasma

The reconstruction problem for steady symmetrical two-dimensional magnetic reconnection is addressed in the frame of a two-fluid approximation with neglected ion current. This approach yields Poisson's equation for the magnetic potential of the in-plane magnetic field, where the right-hand side contains the out-of-plane electron current density with the reversed sign. In the simplest case of uniform electron temperature and number density and neglecting the electron inertia, Poisson's equation turns to the Grad–Shafranov one. With boundary conditions fixed at any unclosed curve (the satellite trajectory), both equations result in an ill-posed problem. Since the magnetic configuration in the reconnection region is highly stretched, one can make use of the boundary layer approximation; hence, the problem becomes well-posed. The described approach is generalized for the case of nonuniform electron temperature and number density. The benchmark reconstruction of the PIC simulations data has shown that the main contribution for inaccuracy arises from replacing Poisson's equation by the equation of Grad–Shafranov. Under this substitution, the reachable cross-size of the reconstructed region is shrinking down to fractions of the proton inertial length. Artificial smoothing, demanded by solving the ill-posed problem, and boundary layer approximation represent two alternative methods of problem regularization. In terms of the reconstruction error, they perform nearly the same; the second method benefits from the comparative simplicity and less restrictions imposed on the boundary shape.

Effects of Radial Distances on Small-scale Magnetic Flux Ropes in the Solar Wind

Abstract Small-scale magnetic flux ropes (SFRs) in the solar wind have been studied for decades. Statistical analysis utilizing various in situ spacecraft measurements is the main observational approach to investigating the generation and evolution of these small-scale structures. Based on the Grad–Shafranov reconstruction technique, we use the automated detection algorithm to build the databases of these small-scale structures via various spacecraft measurements at different heliocentric distances. We present the SFR properties, including the magnetic field and plasma parameters at different radial distances from the Sun near the ecliptic plane. It is found that the event occurrence rate is still of the order of a few hundreds per month, the duration and scale-size distributions follow power laws, and the flux-rope axis orientations are approximately centered around the local Parker spiral directions. In general, most SFR properties exhibit radial decays. In addition, with various databases established, we derive scaling laws for the changes in average field magnitude, event counts, and SFR scale sizes, with respect to the radial distances, ranging from ∼0.3 au for Helios to ∼7 au for the Voyager spacecraft. The implications of our results for comparisons with the relevant theoretical works and for applications to the Parker Solar Probe mission are discussed.

ACR Proton Acceleration Associated with Reconnection Processes beyond the Heliospheric Termination Shock

Abstract One of the curious observations from the Voyagers is that the intensity of anomalous cosmic rays (ACRs) did not peak at the heliospheric termination shock (HTS) but instead a short distance (within ∼1 au) downstream of the HTS. One possible explanation is that the interaction of the wavy heliospheric current sheet with the HTS enhances magnetic reconnection and generates numerous small-scale magnetic flux ropes in the heliosheath immediately downstream of the HTS. Charged particles are accelerated in this region due to Fermi acceleration and the reconnection electric field. In this work, we provide observational evidence of the presence of magnetic flux ropes in the heliosheath region just downstream of the HTS using a wavelet analysis of the reduced magnetic helicity and Grad–Shafranov reconstruction techniques. The Zank et al. kinetic transport theory for particles propagating through the magnetic islands region is employed to fit the observed energetic proton intensities in the post-HTS region. Our modeling results agree reasonably well with the observations, which suggests that stochastic acceleration via reconnection processes can explain the ACR proton peak beyond the HTS.

Analysis of Small-scale Magnetic Flux Ropes Covering the Whole Ulysses Mission.

Small-scale magnetic flux ropes in the solar wind have been studied for decades via both simulation and observation. Statistical analysis utilizing various in situ spacecraft measurements is the main observational approach, which helps investigate the generation and evolution of these small-scale structures. In this study, we extend the automated detection of small-scale flux ropes based on the Grad-Shafranov reconstruction to the complete data set of in situ measurements of the Ulysses spacecraft. We first discuss the temporal variation of the bulk properties of 22,719 flux ropes found through our approach, namely, the average magnetic field and plasma parameters, etc., as functions of the heliographic latitudes and heliocentric radial distances. We then categorize all identified events into three groups based on event distributions in different latitudes separated by 30°, at different radial distances, and under different solar activities. With the detailed statistical analysis, we conclude the following: (1) the properties of flux ropes, such as the duration, scale size, etc., follow power-law distributions, but with different slope indices, especially for distributions at different radial distances. (2) They are also affected by the solar wind speed, which has different distributions under different solar activities, manifested as a latitudinal effect. (3) The main difference in flux rope properties between the low and high latitudes is attributed to possible Alfvénic structures or waves and to flux ropes with relatively high Alfvénicity. (4) Flux ropes with longer durations and larger scale sizes occur more often at larger radial distances. (5) With a stricter Walén slope threshold, more events are excluded at higher latitudes, which further reduces the latitudinal effects on flux rope properties. The entire database is published online at http://www.fluxrope.info.

The Magnetic Field Geometry of Small Solar Wind Flux Ropes Inferred from Their Twist Distribution

This work extends recent efforts on the force-free modeling of large flux rope-type structures (magnetic clouds, MCs) to much smaller spatial scales. We first select small flux ropes (SFRs) by eye whose duration is unambiguous and which were observed by the Solar Terrestrial Relations Observatory (STEREO) or Wind spacecraft during solar maximum years. We inquire into which analytical technique is physically most appropriate. We consider three models: (i) linear force-free field ($\bigtriangledown\times$ B = $\alpha (r) $ B) with a specific, prescribed constant $\alpha$ (Lundquist solution), and (ii) with $\alpha$ as a free constant parameter (Lundquist-alpha solution), (iii) uniform twist field (Gold-Hoyle solution). We retain only those cases where the impact parameter is less than one-half the FR radius, $R$, so the results should be robust (29 cases). The SFR radii lie in the range [$\sim$ 0.003, 0.059] AU. Comparing results, we find that the Lundquist-alpha and uniform twist solutions yielded comparable and small normalized $\chi^2$ values in most cases. We then use Grad-Shafranov (GS) reconstruction to analyze these events further. We then considered the twist per unit length, $\tau$, both its profile through the FR and its absolute value. We find $\tau$ to lie in the range [5.6, 34] turns/AU. The GH model-derived $\tau$ values are comparable to those obtained from GS reconstruction. We find that twist unit length ($L$) is inversely proportional to $R$, as $\tau \sim 0.17/R$. We combine MC and SFR results on $\tau (R)$ and give a relation which is approximately valid for both sets. The axial and azimuthal fluxes, $F_z$ and $F_\phi$, vary as $\approx 2.1 B_0 R^2 \times10^{21}$ Mx and $F_{\phi}/L \approx 0.36 B_0 R \times10^{21}$Mx/AU. The relative helicity per unit length, $H/L \approx 0.75 B_0^2 R^3$$\times 10^{42}$ Mx$^2$/AU.

Analytical model test of methods to find the geometry and velocity of magnetic structures

It is important to determine the dimensionality and velocity information in the study of spatial magnetic structures. Many data analysis theories/techniques are based on the assumption of one or two dimensions. For example, the Grad-Shafranov (GS) reconstruction method assumes a dimensionality of two or less. The Minimum Direction Derivative (MDD) method provides an indication of the dimensionality. For the structure velocity, the components in each dimensionality can be calculated by Spatio-Temporal Difference analysis (STD). In order to improve the convenience of use of MDD method, a new parameter D m quantifying the dimensionality based on MDD eigenvalues is introduced in this paper. The influences of noise /turbulence, separation distance and tetrahedron configuration on MDD and the evaluation of D m are systematically tested using two analytical models for magnetic structures, representing a magnetic mirror and magnetic flux rope. We tested and gave the threshold values of three quality indicators for MDD results using the flux rope model. We also show that the error induced by turbulence is comparable to that of random noise when the turbulence scales are less than the spacecraft separation. Besides, the accuracy of STD velocity estimation will also be influenced by turbulence for cases with excessively high data time resolution. By using D m, we show that an ideal model of a mirror-like structure can be divided into one dimension (1-D) and three dimension (3-D) regions. This restricts the applicability of the GS method in mirror-like structures. For example, in a given reconstruction range, the GS error increased from less than 7% to more than 15% by using the data along trajectories in 1-D and 3-D regions as predicated by D m. Thus, it is important to estimate the structure dimensionality, which can be further used to estimate the reliability of the GS reconstruction map.

Automated Detection of Small-scale Magnetic Flux Ropes in the Solar Wind: First Results from the Wind Spacecraft Measurements

Abstract We have developed a new automated small-scale magnetic flux rope (SSMFR) detection algorithm based on the Grad–Shafranov (GS) reconstruction technique. We have applied this detection algorithm to the Wind spacecraft in situ measurements during 1996–2016, covering two solar cycles, and successfully detected a total number of 74,241 small-scale magnetic flux rope events with duration from 9 to 361 minutes. This large number of small-scale magnetic flux ropes has not been discovered by any other previous studies through this unique approach. We perform statistical analysis of the small-scale magnetic flux rope events based on our newly developed database, and summarize the main findings as follows. (1) The occurrence of small-scale flux ropes has strong solar-cycle dependency with a rate of a few hundred per month on average. (2) The small-scale magnetic flux ropes in the ecliptic plane tend to align along the Parker spiral. (3) In low-speed (<400 km s−1) solar wind, the flux ropes tend to have lower proton temperature and higher proton number density, while in high-speed (≥400 km s−1) solar wind, they tend to have higher proton temperature and lower proton number density. (4) Both the duration and scale size distributions of the small-scale magnetic flux ropes obey a power law. (5) The waiting time distribution of small-scale magnetic flux ropes can be fitted by an exponential function (for shorter waiting times) and a power-law function (for longer waiting times). (6) The wall-to-wall time distribution obeys double power laws with the break point at 60 minutes (corresponding to the correlation length). (7) The small-scale magnetic flux ropes tend to accumulate near the heliospheric current sheet (HCS). The entire database is available at http://fluxrope.info and in machine-readable format in this article.

Observational Analysis of Small-scale Magnetic Flux Ropes from Ulysses In-situ Measurements

Small-scale magnetic flux ropes, which have similar magnetic field configuration as their large-scale counterparts (i.e., magnetic clouds), but with different sizes and origin, constitute an important element of solar wind structures. They are also considered to be associated with local particle energization and other related processes. In this report, we apply the Grad-Shafranov (GS) reconstruction method to detect these small-scale flux ropes with a set of quantitative criteria by utilizing data from the Ulysses spacecraft measurements for the first time. We conduct full range automatic detection for years 1994, 1996, 2004 and 2005 during the solar minimum periods. Based on solar wind speed/helio-latitude ranges, these periods are categorized into two groups: one with high solar wind speeds at high latitudes (1994 and 1996) and the other with low solar wind speeds at low latitudes (2004 and 2005). Through mainly statistical analysis of the results from these four years worth of Ulysses data, we have obtained the following findings: (1) Alfvénic structures occur more frequently at higher latitudes or in high speed solar wind (1994 and 1996). (2) Small-scale flux ropes at lower latitudes tend to align with the nominal Parker spiral direction. (3) The scale sizes of small-scale flux ropes are in the same range for different heliocentric distances. Both scale size and duration distributions seem to obey power laws, similar to the analysis results at 1 astronomical unit (AU). (4) The waiting time distribution (WTD) is fitted well by an exponential function rather than a power law. (5) The power law fitting is applied to the wall-to-wall time distribution with the break point at ∼ 200 min which is 3∼4 times the result at 1 AU.